Approximately 120 people rated the numbers 0-9 on whether they had a feminine or masculine association with that number.
An early paper by Wilkie and Bodenhausen (2015), claimed that people have a feminine association with even numbers, while having a masculine association with odd numbers. Below are the observed data, based on around 130 (n differs per number) bachelor students.
The Bayesian binomial test gives 2 versions of the Bayes factor and prior posterior plot: one for the proportion of "Feminine" responses, and one for the proportion of "Masculine" responses. In correspondence with the original authors' claims (proportion feminine responses > 0.5 for even numbers; proportion masculine responses > 0.5 for odd numbers), we look at the positive Bayes factor (BF+0) for the even numbers, while looking at the positive Bayes factor for the odd numbers. Note that if we would have done a two-sided test (results provided at the end), the Bayes factor (BF10) will be the same for either proportion (masculine/feminine). For each test, we use uninformed prior distribution(beta (a = b = 1).
Based on the Bayes factors below, I would claim that while there is some evidence for a gendered association for some digits, it is not so simple as stating that odd numbers are feminine and even numbers are masculine. Only for the numbers 1 & 2 did we observe very compelling evidence in favor of the theory. For the numbers 0, 3, 7, 9 we observed some degree of evidence in favor of the null (varying from weak to strong evidence). For 4, 5, 6, and 8 we observed some degree of evidence in favor of the theory (varying from weak to strong evidence).
| Level | Counts | Total | Proportion | BF₊₀ | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 | Feminine | 59 | 124 | 0.476 | 0.076 | ||||||
| Masculine | 65 | 124 | 0.524 | 0.182 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 | Feminine | 44 | 128 | 0.344 | 0.023 | ||||||
| Masculine | 84 | 128 | 0.656 | 120.509 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 | Feminine | 84 | 128 | 0.656 | 120.509 | ||||||
| Masculine | 44 | 128 | 0.344 | 0.023 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 | Feminine | 63 | 128 | 0.492 | 0.096 | ||||||
| Masculine | 65 | 128 | 0.508 | 0.127 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 | Feminine | 74 | 126 | 0.587 | 1.469 | ||||||
| Masculine | 52 | 126 | 0.413 | 0.038 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 | Feminine | 47 | 125 | 0.376 | 0.029 | ||||||
| Masculine | 78 | 125 | 0.624 | 10.474 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 | Feminine | 79 | 129 | 0.612 | 5.696 | ||||||
| Masculine | 50 | 129 | 0.388 | 0.031 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 | Feminine | 56 | 127 | 0.441 | 0.049 | ||||||
| Masculine | 71 | 127 | 0.559 | 0.484 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 | Feminine | 77 | 127 | 0.606 | 3.864 | ||||||
| Masculine | 50 | 127 | 0.394 | 0.032 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 | Feminine | 74 | 127 | 0.583 | 1.209 | ||||||
| Masculine | 53 | 127 | 0.417 | 0.039 | |||||||
| Note. For all tests, the alternative hypothesis specifies that the proportion is greater than 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1). | |||||||||||
An interpretation of the Bayes factors, for each of the 10 digits:
Approximately 120 people rated the numbers 0-9 on whether they had a feminine or masculine association with that number.
An early paper by Wilkie and Bodenhausen (2015), claimed that people have a feminine association with even numbers, while having a masculine association with odd numbers. Below are the observed data, based on around 130 (n differs per number) bachelor students.
The Bayesian binomial test gives 2 versions of the Bayes factor and prior posterior plot: one for the proportion of "Feminine" responses, and one for the proportion of "Masculine" responses. In correspondence with the original authors' claims (proportion feminine responses > 0.5 for even numbers; proportion masculine responses > 0.5 for odd numbers), we look at the positive Bayes factor (BF+0) for the even numbers, while looking at the positive Bayes factor for the odd numbers.
Based on the Bayes factors below, I would claim that while there is some evidence for a gendered association for some digits, it is not so simple as stating that odd numbers are feminine and even numbers are masculine. Only for the numbers 1 & 2 did we observe very compelling evidence in favor of the theory. For the numbers 0, 3, 7, 9 we observed some degree of evidence in favor of the null (varying from weak to strong evidence). For 4, 5, 6, and 8 we observed some degree of evidence in favor of the theory (varying from weak to strong evidence).
| Level | Counts | Total | Proportion | BF₁₀ | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 0 | Feminine | 59 | 124 | 0.476 | 0.129 | ||||||
| Masculine | 65 | 124 | 0.524 | 0.129 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 1 | Feminine | 44 | 128 | 0.344 | 60.266 | ||||||
| Masculine | 84 | 128 | 0.656 | 60.266 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 2 | Feminine | 84 | 128 | 0.656 | 60.266 | ||||||
| Masculine | 44 | 128 | 0.344 | 60.266 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 3 | Feminine | 63 | 128 | 0.492 | 0.112 | ||||||
| Masculine | 65 | 128 | 0.508 | 0.112 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 4 | Feminine | 74 | 126 | 0.587 | 0.753 | ||||||
| Masculine | 52 | 126 | 0.413 | 0.753 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 5 | Feminine | 47 | 125 | 0.376 | 5.251 | ||||||
| Masculine | 78 | 125 | 0.624 | 5.251 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 6 | Feminine | 79 | 129 | 0.612 | 2.863 | ||||||
| Masculine | 50 | 129 | 0.388 | 2.863 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 7 | Feminine | 56 | 127 | 0.441 | 0.267 | ||||||
| Masculine | 71 | 127 | 0.559 | 0.267 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 8 | Feminine | 77 | 127 | 0.606 | 1.948 | ||||||
| Masculine | 50 | 127 | 0.394 | 1.948 | |||||||
| Rate each of the numbers 0-9 on whether you have a feminine or masculine association | 9 | Feminine | 74 | 127 | 0.583 | 0.624 | ||||||
| Masculine | 53 | 127 | 0.417 | 0.624 | |||||||
| Note. Proportions tested against value: 0.5. The shape of the prior distribution under the alternative hypothesis is specified by Beta(1, 1). | |||||||||||
An interpretation of the Bayes factors, for each of the 10 digits: